Transition to chaos in the «reaction–diffusion» systems. The simplest models

Malinetsky G.G., Faller D.S.
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The article discusses the emergence of chaotic attractors in the system of three ordinary differential equations arising in the theory of «reaction-diffusion» systems. The dynamics of the corresponding one- and two-dimensional maps and Lyapunov exponents of such attractors are studied. It is shown that the transition to chaos is in accordance with a non-traditional scenario of repeated birth and disappearance of chaotic regimes, which had been previously studied for one-dimensional maps with a sharp apex and a quadratic minimum. Some characteristic features of the system — zones of bistability and hyperbolicity, the crisis of chaotic attractors — are studied by means of numerical analysis.

Keywords: nonlinear dynamics, «reaction–diffusion» systems, bifurcation, self-similarity, «cascade of cascades», attractor crisis, ergodicity, bistability
Citation in English: Malinetsky G.G., Faller D.S. Transition to chaos in the «reaction–diffusion» systems. The simplest models // Computer Research and Modeling, 2014, vol. 6, no. 1, pp. 3-12
Citation in English: Malinetsky G.G., Faller D.S. Transition to chaos in the «reaction–diffusion» systems. The simplest models // Computer Research and Modeling, 2014, vol. 6, no. 1, pp. 3-12
DOI: 10.20537/2076-7633-2014-6-1-3-12
URL: http://crm-en.ics.org.ru/journal/article/2113/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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